{
  "id": "2112.14268",
  "version": "v2",
  "published": "2021-12-28T19:07:37.000Z",
  "updated": "2022-07-10T10:20:43.000Z",
  "title": "On the existence of $B$-root subgroups on affine spherical varieties",
  "authors": [
    "Roman Avdeev",
    "Vladimir Zhgoon"
  ],
  "comment": "v2: 7 pages, minor corrections",
  "journal": "Doklady Mathematics, vol. 105 (2022), no. 2, 51-55",
  "doi": "10.1134/S1064562422020053",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be an irreducible affine algebraic variety that is spherical with respect to an action of a connected reductive group $G$. In this paper we provide sufficient conditions, formulated in terms of weight combinatorics, for the existence of one-parameter additive actions on $X$ normalized by a Borel subgroup $B \\subset G$. As an application, we prove that every $G$-stable prime divisor in $X$ can be connected with the open $G$-orbit by means of a suitable $B$-normalized one-parameter additive action.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-07-10T10:20:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14R20",
      "14M27",
      "13N15"
    ],
    "keywords": [
      "affine spherical varieties",
      "root subgroups",
      "irreducible affine algebraic variety",
      "sufficient conditions",
      "normalized one-parameter additive action"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}